dcf-lab

A discounted cash flow produces one number, and the number is usually discussed as though the forecast years had produced it. They often did not. The perpetuity attached after the last forecast year is frequently the larger half of the answer. Nothing in a spreadsheet says so: the enterprise value sits in one cell and carries no record of which part of the model it came from.

The second failure is quieter. Terminal growth and the cost of capital are typed into adjacent cells with nothing between them. Set the growth rate at or above the discount rate and the Gordon formula divides by zero or by a negative number, and the spreadsheet returns something anyway: a negative enterprise value, or a very large positive one that reads like an argument. A model that answers there is worse than a model that stops.

Discounted cash flow with the terminal value split out and reported as a share. Five forecast cash flows are discounted on the end year convention, each at a full year. The terminal value is the Gordon growth perpetuity taken at the end of year five and brought back with the same year five discount factor. The enterprise value is the sum of the two parts. The headline the instrument prints is not the enterprise value but the fraction of it that the perpetuity contributes.

PV(t)   = FCF(t) / (1 + w)^t              for t = 1 to 5
TV      = FCF(5) × (1 + g) / (w - g)
PV(TV)  = TV / (1 + w)^5
EV      = PV(1) + ... + PV(5) + PV(TV)
share   = PV(TV) / EV

refused when g is at or above w

Two sliders and nothing else to type. Everything below them is recomputed on every movement: the headline share, a single bar split between the forecast present value and the terminal present value, a table of the five years with their discount factors, and one line of arithmetic that writes the terminal value out with its numbers substituted in.

It refuses to value a perpetuity that grows at or faster than the rate discounting it. Push terminal growth up to the cost of capital and the instrument prints Refused and no enterprise value at all. The reason stands next to the refusal: a perpetuity growing at or above its discount rate has unbounded value, so there is no number to report.

It refuses the usual repair. Clamping growth to just under the cost of capital would keep the model producing output, and the output would be worthless: the clamp swaps in a different model whose answer runs away as the clamp tightens. The refusal says which of the two inputs must be wrong and leaves the choice to the person who typed them.

The refusal is narrow on purpose. In that state the five forecast years still discount normally, and the instrument says so in its own note. It is only the perpetuity that has no answer, and it does not take the rest of the model down with it.

It refuses to be a valuation. There is no net debt, no share count, no currency and no per share figure, and the cash flows cannot be edited. The one question it answers is how much of an enterprise value the perpetuity carries. Everything that would turn that into a price is deliberately absent, because a price would invite the reader to trust it.